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Kelvin's Circulation Theorem

Mathematical Physics

Kelvin's Circulation Theorem states that in an inviscid, barotropic fluid acted on only by conservative forces, the circulation around a closed material loop that moves with the fluid stays constant over time. Named for William Thomson, Lord Kelvin, it is a foundational result of fluid dynamics explaining why vortices in an ideal fluid, once formed, persist rather than spontaneously appearing or dissipating, and it underlies the later Helmholtz theorems on vortex lines.

Facts
Statement
In a barotropic, ideal fluid with conservative body forces, the circulation around a closed curve (which encloses the same fluid elements) moving with the fluid remains constant with time. 1
Proof Year
1869 1
Classification
Statement Form
Identity or Equation 1
Connections

Has Statement Form

Equation, Concepts
Identity, Concepts

In Branch

Source Kelvin's circulation theorem (Wikipedia)
Sources
1. Kelvin's circulation theorem (Wikipedia)
  • Statement of the theorem
    In a barotropic, ideal fluid with conservative body forces, the circulation around a closed curve (which encloses the same fluid elements) moving with the fluid remains constant with time.
  • Naming and publication
    The theorem is named after William Thomson, 1st Baron Kelvin who published it in 1869.
  • In Group: Electromagnetism, Optics and Continuum Mechanics, Lead section
    In fluid mechanics, Kelvin's circulation theorem states:In a barotropic
  • In Branch: Mathematical Physics, Lead section
    In fluid mechanics, Kelvin's circulation theorem states:In a barotropic
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